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In set theory, a mathematical discipline, the Jensen hierarchy or J-hierarchy is a modification of Gödel's constructible hierarchy, L, that circumvents certain technical difficulties that exist in the constructible hierarchy. The J-Hierarchy figures prominently in fine structure theory, a field pioneered by Ronald Jensen, for whom the Jensen hierarchy is named. ==Definition== As in the definition of ''L'', let Def(''X'') be the collection of sets definable with parameters over ''X'': : Def(''X'') = . The constructible hierarchy, L is defined by transfinite recursion. In particular, at successor ordinals, ''L''α+1 = Def(''L''α). The difficulty with this construction is that each of the levels is not closed under the formation of unordered pairs; for a given x, y ε ''L''α+1 − ''L''α, the set will not be an element of ''L''α+1, since it is not a subset of ''L''α. However, ''L''α does have the desirable property of being closed under Σ0 separation. Jensen's modified hierarchy retains this property and the slightly weaker condition that , but is also closed under pairing. The key technique is to encode hereditarily definable sets over ''J''α by codes; then ''J''α+1 will contain all sets whose codes are in ''J''α. Like ''L''α, ''J''α is defined recursively. For each ordinal α, we define to be a universal Σn predicate for ''J''α. We encode hereditarily definable sets as , with . Then set ''J''α, n to be . Finally, ''J''α+1 = . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Jensen hierarchy」の詳細全文を読む スポンサード リンク
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